Abstract. In this article we continue our analysis of Schr dinger operators with a random
potential using scattering theory. In particular the theory of Krein's spectral
shift function leads to an alternative construction of the density of states in
arbitrary dimensions. For arbitrary dimension we show existence of the spectral
shift density, which is defined as the bulk limit of the spectral shift
function per unit interaction volume. This density equals the difference of the
density of states for the free and the interaction theory. This extends the
results previously obtained by the authors in one dimension. Also we consider
the case where the interaction is concentrated near a hyperplane.